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Applications of Fractals

The fractals have more and more applications in the science. The main reason is that they describe very often better the real world than traditional mathematics and physics.

Some example are presented in this page.

arrAstronomy
arrComputer science
arrFluid mechanics
arrTelecommunications
arrSurface physics
arrMedicine
 

Astronomy

Fractals will maybe revolutionize the way to see the universe (ref.1 and ref.3). Cosmologists usually assume that matter is spread uniformly across space. But observation shows this is not true. Astronomers agree with that fact on "small" scales, but most of them think that the universe is smooth at very large scales. However, a dissident group of scientists claims that the structure of the universe is fractal at all scales. If this new theory is proved to be correct, even the big bang models should be adapted. But at present, cosmologists need more data about the matter distribution in the universe to prove (or not) that we are living in a fractal universe. More on the debate is here.
 

Computer science

Actually, the most useful use of fractals in computer science is the fractal image compression. This kind of compression uses the fact that the real world is well described by fractal geometry. By this way, images are compressed much more than by usual ways (eg: JPEG or GIF file formats). An other advantage of fractal compression is that when the picture is enlarged, there is no pixelisation. The picture seems very often better when its size is increased.
 

Fluid mechanics

  • The study of turbulence in flows is very adapted to fractals. Turbulent flows are chaotic and very difficult to model correctly. A fractal representation of them helps engineers and physicists to better understand complex flows.
  • Flames can also be simulated.
  • Porous media have a very complex geometry and are well represented by fractal. This is actually used in petroleum science.

 

Telecommunications

A new application is fractal-shaped antennae that reduce greatly the size and the weight of the antennas (ref.1). Fractenna is the company which sells these anteennae.
 

Surface physics

Fractals are used to describe the roughness of surfaces. A rough surface is characterized by a combination of two different fractals.
 

Medicine

Biosensor interactions can be studied by using fractals.
 

References:

1. "Fractured Universe", New scientist, 21 August 1999
2. "Aerial magic", May Mike, New scientist, 31 January 1998
3. "Is the universe a fractal?", New scientist, 9 March 2007
 


Copyright 1998-2017 Philippe Wautelet